MCS640 Thermal Imager Manual Principle of Thermal Imaging • 31
If all energy falling on an object were absorbed (no transmission or reflection), the absorptivity would equal to
1. At a steady temperature, all the energy absorbed could be re-radiated (emitted) so that the emissivity of
such a body would equal 1. Therefore in a blackbody,
absorptivity = emissivity = 1
Practical real life objects do not behave exactly as this ideal, but as described with transmissivity and
reflectivity,
absorptivity + transmissivity + reflectivity = 1
Planck’s Law
Energy radiated from the blackbody is described as follows [“Planck’s
Law”.]
Stefan Bolzmann’s
equation
In order to obtain total radiant emittance of the blackbody, integrate the
equation (1) through all wavelengths (0 to infinity). The result is as follows
and is called “Stefan-Bolzmann equation.”
Wien’s displacement law
The temperature of blackbody can be obtained directly from the radiant
energy of the blackbody by this equation. In order to find out the
wavelength on the maximum spectral radiant emittance, differentiate
Planck’s law and take the value to 0.
The equation is called “Wien’s displacement law”.
Where in (1) to (3),
In radiation of a normal object, as the emissivity is (<1) times of the blackbody, multiply above equation by the
emissivity. The following figures show the spectral radiant emittance of a blackbody.
(a) is shown by logarithmic scale and (b) is shown by linear scale.
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